US20030173864A1 - Heat pumped parametric MEMS device - Google Patents

Abstract

A micro-electrical mechanical oscillator has a resonant frequency of oscillation that is varied by application of heat. The resonant frequency is varied at a frequency different from the resonant frequency of the oscillator to amplify oscillations. In one embodiment, the oscillator is disc of material supported by a pillar of much smaller diameter than the disc. The periphery of the disc is heated by a laser to provide a time varying shift of the resonant frequency (or equivalently the stiffness) of the disc. Feedback from movement of the disc is used to modulate the intensity of the laser, and thus the stiffness of the disc to provide parametric amplification of sensed vibrations, using heating as a pump. Various other shapes of micro-electrical mechanical oscillators are used in other embodiment, including an array of such oscillators on a substrate, each having different resonant frequencies.

Description

GOVERNMENT FUNDING
• [0001] The invention described herein was made with U.S. Government support under Grant Number DMR-0079992 awarded by National Science Foundation. The United States Government has certain rights in the invention.
FIELD OF THE INVENTION
• The present invention relates to microelectromechanical systems (MEMS) and in particular to heat pumped parametric MEMS devices.[0002]
BACKGROUND OF THE INVENTION
• A conventional electrical amplifier is essentially a variable resistance that uses energy from a direct current (DC) source to increase alternating current (AC) energy. A parametric amplifier uses a nonlinear variable reactance, such as capacitance that varies with time, to supply energy from an AC source to a load. The energy required to vary the capacitance is obtained from an electrical source called a pump. Since reactance does not add thermal noise to a circuit, parametric amplifiers produce less noise than most conventional amplifiers.[0003]
• Dynamic properties of mechanical resonators can be utilized to create a parametric amplifier. Parametric amplification has long been used as a technique for making a low noise electronic amplifier. The amplification of the applied signal is done by making use of energy from the pump. Parametric amplifiers with a variable-capacitance main-oscillator semiconductor diode are used in radar tracking and communications between Earth stations, satellites, and deep-space stations. The noise temperature of cooled amplifiers is in the range of 20 to 30 K, and the gains are up to 40 dB. This type of amplification is also widely used in optics as well as in electronic traveling wave applications. Parametric amplification is also observed in microelectromechanical systems (MEMS).[0004]
• Scaling down the dimensions of MEMS into the micron and submicron region shortens the response time down to nanoseconds. A bar clamped at both ends with dimensions 0.2×0.2×2 microns microfabricated from single-crystal silicon exhibits a resonant frequency of 380 MHz, extending the area of MEMS applications into the ultra-high frequency (UHF) region. UHF MEMS devices are expected to replace bulky and power-hungry elements in telecommunication devices, such as quartz oscillators, filters, frequency converters, etc. Since the process of MEMS fabrication is compatible with modern silicon technology, micromechanical devices can be the basis for next generation UHF integrated circuits.[0005]
• However, the way to transform an electrical signal into mechanical motion and vice versa represents one of the main challenges in MEMS applications. In the most straightforward filter configuration, a MEMS oscillator would be driven electrostatically by an external voltage V[0006]_ext(signal from antenna), exhibiting mechanical vibrations when V_exthas a resonating frequency component. Such an UHV mechanical vibration with nanometer amplitude must be converted back into an electric signal for further processing.
• The high frequency of the mechanical motion practically excludes supersensitive but slow detection methods, such as electron tunneling, used in accelerometry or magnetometry. Capacitive and optical detection methods are considered as the most suitable because of their fast response and high sensitivity. An optical method employing a focused laser beam allows a design not overloaded by closely placed electrodes, and also provides reduced cross-talk between driving and detection signals. Interferometric and beam-deflection techniques convert the intensity variation of the reflected laser beam (caused by mechanical motion) into electrical signal with subsequent amplification and measurement by an electric circuit.[0007]
• Laser wavelength puts a limit on the sensitivity of the interferometric method, making detection of nanometer motion problematic. Signal processing (amplification in this case) on the mechanical level, provided before the mechanic-to-electric conversion by an active UHF micromechanical component, can solve such a problem and is considered as a key point for future MEMS devices.[0008]
• Parametric amplification represents a means for “mechanical signal processing” in regards to MEMS oscillators. The energy, necessary to gain mechanical motion is provided by periodic modulation of the oscillator's parameter—effective stiffness k. Small mechanical vibrations, induced by a weak external force can be amplified by the parametric mechanism and the enhanced vibrations will be detected optically. Since a “mechanical parametric preamplifier” can be noise-free down to the quantum-mechanical level, it should greatly improve the signal-to-noise ratio of the resulting signal. A mechanical oscillator embedded in a degenerate parametric amplification scheme is also fundamentally interesting because mechanical squeezed states can be produced by such a system: the thermal vibration in one phase of the response can be reduced below the thermal equilibrium level. In MEMS oscillators, the only method that has demonstrated parametric amplification is achieved by modulation of the effective spring constant by superimposing a time-varying electric field between the oscillator and an additional, closely located capacitor plate.[0009]
SUMMARY OF THE INVENTION
• A micromechanical oscillator has a resonant frequency defined by an effective spring constant that is modified by application of heat. The resonant frequency is varied at a frequency different from the resonant frequency of the oscillator to amplify oscillations. In one embodiment, the oscillator is disc of material supported by a pillar of much smaller diameter than the disc. The periphery of the disc is heated by a laser to provide a time varying shift of the resonant frequency (or equivalently the spring constant or stiffness) of the disc.[0010]
• A reference signal is used to modulate the intensity of the laser in one embodiment, and thus the stiffness of the disc to provide parametric amplification of sensed vibrations, using heating as a pump. Feedback from movement of the disc is used in a further embodiment.[0011]
• A method of making an oscillator comprises forming a first sacrificial layer on a substrate followed by a disc layer on top of the first layer. A disc is then formed in the disc layer and the first layer is undercut to form a pillar supporting the disc above the substrate. In one embodiment, the sacrificial layer is formed of silicon oxide and the disc layer is formed of single crystal silicon. Hydrofluoric acid is used to undercut the first layer.[0012]
• In use, the disc is heated such as by a laser, and vibration of the disc is sensed. The modulation of the intensity of the heating is based on the sensed vibration or a reference signal. In one embodiment, a lower power laser, having a power below a self generation threshold is used to form an amplifier. In a further embodiment, a power level above the self generation threshold is used to form a generator. No variation of laser intensity is required in the generator embodiment.[0013]
• An alternative method of sensing vibrations comprises locating one of many different types of micromechanical oscillators proximate a vibrating surface and changing an effective stiffness of the micromechanical oscillator. A reference signal, or vibration of the micromechanical oscillator is sensed and used to modulate the effective stiffness of the oscillator to provide parametric feedback.[0014]
• In further embodiments, the MEMS oscillator is utilized as an amplifier, antenna, phase demodulator, receiver and laser controlled oscillator. In a receiver embodiment, multiple MEMS of various sizes and hence different resonant frequencies, are located near each other, such as on a substrate. The laser is directed to one of the MEMS depending on the frequency to be received. In further embodiments, the MEMS are formed on a semiconductor substrate, and share a junction, such as a pn junction used to conduct signals.[0015]
• In still a further embodiment, a bridge structure is used as an oscillator. An AC current is run through the bridge to vary its effective stiffness at a frequency approximately twice the resonant frequency of oscillation of the bridge structure.[0016]
BRIEF DESCRIPTION OF THE DRAWINGS
• FIG. 1 is a block diagram of a MEMS structure for use as a heat pumped parametric oscillator.[0017]
• FIGS. 2A, 2B, and[0018]2C illustrate a process of forming the MEMS structure of FIG. 1.
• FIG. 3 shows a test structure used to test the MEMS structure of FIG. 1.[0019]
• FIG. 4 illustrates three modes of vibrations for the MEMS structure of FIG. 1.[0020]
• FIG. 5 is a block schematic diagram of a MEMS oscillator configured as a phase locked amplifier[0021]
• FIGS. 6A and 6B are block/schematic diagrams of the MEMS oscillator used as a receiver with an antenna.[0022]
• FIG. 7 illustrates a MEMS oscillator used in a homodyne receiver.[0023]
• FIG. 8 illustrates the use of an interferometric pattern to modulate heat absorption in an MEMS oscillator.[0024]
DETAILED DESCRIPTION OF THE INVENTION
• In the following description and the drawings illustrate specific embodiments of the invention sufficiently to enable those skilled in the art to practice it. Other embodiments may incorporate structural, logical, electrical, process, and other changes. The term MEMS is used interchangeably with micromechanical to represent a class of very small mechanical devices either with or without electrical characteristics. Examples merely typify possible variations. Individual components and functions are optional unless explicitly required, and the sequence of operations may vary. Portions and features of some embodiments may be included in or substituted for those of others. The scope of the invention encompasses the full ambit of the claims and all available equivalents. The following description is, therefore, not to be taken in a limited sense, and the scope of the present invention is defined by the appended claims.[0025]
• FIG. 1 is a side view representation of a[0026]micromechanical oscillator100. It oscillates in the radio frequency (RF) range and is fabricated in the form of a silicon disc1110 supported by an SiO₂pillar120 at the disc center. Other shapes, such as oval or polygons may also be used, and are included in the use of the term disc. An effective spring constant of thisoscillator100 is controlled within the range Δf/f˜10⁻⁴by a low power laser beam (P_laser˜100 μW)125, focused at theperiphery130 of the disc. Parametric amplification of the disc's vibrations is achieved through a double frequency modulation of the laser power.
• In some embodiments, amplitude gains are generally limited by non-linear behavior and self-generation. Phase dependence of the gain inherent in degenerate parametric amplification is also observed. Self-modulation of the CW laser beam (P[0027]_laser˜100 μW) provided by placing the disc oscillator into an interference pattern setup can lead to parametric self-excitation.
• Oscillators in the RF range are provided. Generally, the smaller the structure, the higher the frequency of oscillation. Modulating the intensity of the[0028]focused laser beam125 provides periodic (at double frequency) changes of the effective spring constant of the oscillator. The dc component of the laser beam is used to detect the vibration (at the fundamental frequency) by interferometric effects. Optical pumping for parametric amplification does not require the oscillator to be conducting and does not need additional electrodes located in proximity to the oscillator. Existing optical detection techniques are easily integrated.
• A high quality factor (Q) of the oscillator minimizes the amount of heat required for temperature-related effects noticeable. Avoiding points with high local stress concentration and minimizing clamping losses help to enhance the Q. Cylindrically symmetric oscillators such as discs supported by a single pillar at the center point enhance the Q. Minimizing the diameter of the supporting rod results in the disc approaching the equivalent of a free disc.[0029]
• In still a further embodiment, a bridge structure is used as an oscillator. MEMS bridge structures are well known in the art. In this embodiment, an AC current is run through the bridge to vary its effective stiffness at a frequency approximately twice the resonant frequency of oscillation of the bridge structure.[0030]
• As illustrated in FIG. 2A, commercially available silicon-on-insulator (SOI)[0031]wafers210 with a 250 nmthick silicon layer215 on top of a 1 micronsilicon oxide layer220 are used in one embodiment for microfabrication. Other thicknesses of the layers are used in various embodiments to produce oscillators that have different resonant frequencies. Discs of radius R from 5 to 20 microns are defined by electron-beam lithography followed by a dry etch through the top silicon layer as shown in FIG. 2B. The radius of the discs also affects the resonant frequency. Dipping the resulting structure into hydrofluoric acid undercuts the silicon oxide starting from the disc's periphery toward the center as shown in FIG. 2C. By timing this wet etch, the diameter of the remaining column of thesilicon oxide230, which supports the releasedsilicon disc235, is varied. In one embodiment, the diameter of the column is approximately 6.7 microns.
• After a well-known critical point drying (CPD) process using compressed liquefied gas such as CO2 to push out Ethanol. In one embodiment, fabricated[0032]oscillators310 are glued on apiezoceramic transducer320 as shown in FIG. 3. For testing, thetransducer320 is placed into a high vacuum chamber (P=10⁻⁷Torr). An AC voltage applied to a piezoceramic transducer, attached to the wafer, is used to excite the MEMS oscillators. These oscillations result in the variation of the gap between the disc and the silicon substrate and are detected by an interferometric technique with an He—Ne laser beam325 focused on the surface of the disc bylenses330. Abeam splitter335 andlens340 are used to focus reflected light onto an AC coupledphotodetector345, which provide input to aspectrum analyzer350.
• The following analysis of the signals is shown only to illustrate one possible manner in which the oscillators function. It is not represented as providing an exact model of the operation of the oscillators.[0033]
• Plate vibrations are described by the fourth-order differential equation:[0034]$\begin{array}{cc}{\nabla }^4\eta +\frac{3\rho \left(1-s^2\right)}{E{\mathrm{<figure-callout\; label="h"\; filenames="US20030173864A1-20030918-D00002.png"\; state="\{\{state\}\}">h</figure-callout>}}^2}\frac{{\partial }^2\eta }{\partial {\mathrm{<figure-callout\; label="t"\; filenames="US20030173864A1-20030918-D00002.png"\; state="\{\{state\}\}">t</figure-callout>}}^2}=0& \left(1\right)\end{array}$

  
• where E is a flexural modulus, s is Poisson's ratio, ρ is the density of the material and h is half-thickness of the plate. Possible solutions of the equation (1) are given by the expressions:[0035]$\begin{array}{cc}Y\left(r,\varphi \right)=\underset{\sin }{\overset{\cos }{}}\left(m\varphi \right)\left[{\mathrm{AJ}}_m\left(\gamma r\right)+{\mathrm{BI}}_m\left(\gamma r\right)\right]& \left(2\right)\end{array}$

  
• Coefficients A, B and γ[0036]_mnare defined by choosing boundary conditions (displacement and first derivative should be zeroed around the pillar while no bending or shearing forces exist on circumference of the disc). FIG. 4 illustrates three modes of vibrations corresponding to γ₁₀, γ₀₀and γ₂₀marked as1,2,3 respectively. For the structure (R=20 μm, r=6.7 μm), the highest quality factor 11,000 is observed for the mode γ₀₀of the disc oscillations with a frequency of 0.89 MHz.
• A low power laser beam (He—Ne, P[0037]_incident˜100 μW) focused on the periphery of the disc is an effective tool to control the resonant frequency of the disc oscillator. Modes γ₀₀and γ₁₀demonstrate linear increase of the stiffness with the increased laser power, which is quite counterintuitive. At the same time, an expected decrease of the resonant frequency (i.e., softening) is observed for the high-frequency mode γ₂₀.
• Analysis of the thermal stress induced within the disc by the focused laser beam provides the explanation of the observed resonant frequency behavior. For qualitative understanding, consider a simpler problem, a cylinder heated uniformly, with the inner diameter constrained, i.e., the displacement equals zero. (This models the constraint effect that the oxide pillar has on the Si disk.) One can solve this problem in two steps. First heat the cylinder and allow it to expand stress free. Then negative pressure should be applied to pull the inner diameter back to its starting dimension. This tension shifts the resonant frequency of the disc vibration.[0038]
• Modulation of the laser beam intensity provides periodic change of the effective stiffness. Time-varying parameter causes mixing of two different modes of vibrations (in a same way as non-linear circuit provides mixing of two different modes of vibrations). That mixing allows energy supplied to the system at one frequency to be converted to another. For the case of degenerate parametric amplifier, the modes to be coupled are two counter-rotating ones. Providing pumping frequency equal to the sum of the frequencies (which is a double frequency for the degenerate case), the pumping energy is fed into vibration at the fundamental frequency.[0039]
• The high quality factor of the oscillator implies that small energy losses due to internal friction, clamping losses, etc. could be compensated by some low power external source of energy, leading to enhanced mechanical oscillations. Gain dependence on the phase shift φ between stiffness modulation Δk(t) and driving force F(t), following from the equation is also obvious from energetic consideration. In order to provide amplitude gain, the increase of the stiffness Δk should occur around maximum of deflection, thus contributing to potential energy E[0040]_p=(k+Δk)x².
• In one example, synchronization of the stiffness modulation with the motion of the oscillator was achieved by using the ac piezodrive voltage V[0041]_piezoas a reference signal. A schematic diagram is shown in FIG. 5. Anexternal generator510 produces a double frequency ac voltage, phase locked with V_piezo. This voltage after amplification and phase shift is used to control an electro-optical modulator520 (EOM), which, by partial modulation, provides the double-frequency ac component of the intensity of a He—Ne laser beam530 focused on a <5micron spot540 on the surface of thedisc oscillator550 mounted on aPiezo drive560. With this parametric drive, approximately a thirty times increase of the amplitude of the mechanical vibrations was detected, when the ac component of the laser beam was increased to 100 microWatt (the AC power absorbed by the disc can be estimated as approximately 25 microWatt). With a fixed amplitude of the optical pump (fixed gain of the parametric amplification) the system demonstrates linear mechanical response to the piezodriving voltage. The maximum observable gain is limited by the self-generation of the system. Focus of the laser beam at the periphery of the disc appears to provide the best conditions for amplification.
• Heat absorption and thermal stress-induced stiffness modulation are the dominant mechanisms by which the laser beam interacts with the oscillator. Temperature-induced strain could be also accompanied by the stress created by photo-generated carriers. This photo-induced stress in MEMS oscillator can be considered as another way to provide parametric amplification at high frequencies and low light intensity. By optimizing the laser wavelength and using a multilayer design for the oscillator, one can significantly reduce the necessary laser power.[0042]
• Periodic modulation of the laser beam provides time-varying stiffness of the oscillator. It is achieved by an external electro-optical modulator in one embodiment. However, the disc is part of an interferometric device, the gap between the disc and substrate affects the light intensity within the cross section of the disc (and hence—absorbed heating power) by changing interference conditions for reflected beams. Oscillation of the disc (initiated thermally for example) can cause modulation of the local disc heating even for CW laser beam. Non-linear dependence of the heating power versus gap value provides the presence of the second harmonic, necessary for parametric amplification. Phase shift between original mechanical vibrations and light modulation depends on the initial position of the disc within interferometric fringes. If starting conditions and laser beam intensity are chosen properly—self-amplification up to generation will occur.[0043]
• FIGS. 6A and 6B are block/schematic diagrams of the resonator driven by electromagnetic waves. The oscillator serves as an antenna, amplifier and phase demodulator. An[0044]antenna610 provides an electromagnetic excitation signal to adisc oscillator618. Anexternal generator620 produces a double frequency ac voltage. This voltage after amplification and phase shift is used to control an electro-optical modulator625 (EOM), which, by partial modulation, provides the double-frequency ac component of the intensity of a He—Ne laser beam630 focused on a <5micron spot640 on the surface of thedisc oscillator618. Abeam splitter650 provides light reflected from the disc to aphotodetector655 having an output signal provided to anamplifier660.
• FIG. 6B is a schematic diagram of the configuration, illustrating its operation as a phase detector with an external phase-lock loop for frequency demodulation.[0045]
• FIG. 7 illustrates a homodyne MEMS based receiver. An array of various[0046]size MEMS oscillators710,712,714,716,718, and720 are shown mounted on a substrate. Anantenna730 receives RF signals and provides them through alow noise amplifier740 to drive amicrowave strip line750, providing an oscillating electric field to drive the oscillators. Alaser beam760 is focused on a selected oscillator disc to effectively tune the receiver to the resonant frequency of the disc. In one embodiment, apn junction770 is coupled to each oscillator to provide signals from the selected oscillator to aninventor780 for providing an amplified output of the receiver.
• FIG. 8 shows a portion of disc oscillator having a[0047]peripheral portion810 deflecting through an interferometric pattern represented at820. Heat absorption is modulated by motion through the interferometric pattern as theperipheral portion810 deflects through it. Modulation occurs at twice the frequency of the mechanical motion of theperipheral portion810. No external modulation is required, and autoparametric excitation is obtained.
CONCLUSION
• Parametric amplification with optical pumping was realized for radio frequency MEMS oscillator. A gain of 30 and effective quality factor Q=65,000 are demonstrated. Incorporation of parametric amplification into a signal processing for UHF MEMS devices is considered as a main goal. More generally, the parametrical amplification, described in this paper is a method to be used when small mechanical vibrations need to be detected. An enhanced quality factor and amplitude-phase dependence of a light-driven oscillator can be utilized for filtering, or when precise measurements of the frequency are necessary (for example, mass detection experiments). Parametric self-excitation of the MEMS oscillator by CW laser beam was demonstrated for the first time.[0048]

Claims (31)

1. A micro-electrical mechanical resonator comprising:

a substrate;

a vibrating plate;

a pillar supporting the vibrating plate above the substrate.

2. The device ofclaim 1 and further comprising a laser positioned to heat the plate.

3. The device ofclaim 2 wherein the laser provides a beam having a varying intensity and is focused near the periphery of the plate.

4. The device ofclaim 3 wherein the plate has a resonant frequency, and wherein the varying intensity of the beam is approximately twice the resonant frequency.

5. The device ofclaim 4 with laser power below self generation threshold comprising a resonance force sensor.

6. The device ofclaim 4 with laser power above the self generation threshold comprising a generator.

7. The device ofclaim 1 wherein the plate comprises a bridge and AC current is used to modify the temperature of the bridge to modify its effective spring constant.

8. The device ofclaim 1 wherein the substrate is coupled to a vibrating transducer.

9. The device ofclaim 8 wherein the transducer comprises a piezoceramic transducer.

10. The device ofclaim 1 and further comprising:

a varying intensity laser positioned to heat the plate;

a sensor that senses motion of the plate; and

a frequency multiplier driving the variation of the intensity of the laser based on the sensed motion of the plate.

11. A method of making an oscillator, the method comprising:

forming a sacrificial layer on a substrate;

forming a disc layer on top of the sacrificial layer;

forming a disc in the disc layer; and

undercutting the stop layer to form a pillar supporting the disc above the substrate.

12. The method ofclaim 11 wherein the disc layer is formed of single crystal silicon.

13. The method ofclaim 11 wherein the sacrificial layer is silicon oxide.

14. The method ofclaim 11 wherein hydrofluoric acid is used to undercut the sacrificial layer.

15. A method of providing parametric excitation to a micromechanical oscillator, the method comprising:

locally heating the micromechanical oscillator; and

varying the effective spring constant of the oscillator by modulation of the intensity of the local heating based on a sensed oscillation of the micromechanical oscillator or reference signal.

16. A method of increasing oscillation of a micromechanical oscillator, the method comprising:

determining the resonant frequency of the micromechanical oscillator; and

locally heating the micromechanical oscillator at approximately twice its resonant frequency at a position on the micromechanical oscillator that causes a variation in the resonant frequency.

17. A method of sensing vibrations, the method comprising:

locating a micromechanical oscillator proximate a vibrating surface;

locally heating the micromechanical oscillator;

sensing vibration of the micromechanical oscillator; and

modulating the intensity of the local heating based on the sensed vibration.

18. The method ofclaim 17 wherein the micromechanical oscillator comprises a disc supported by a pillar coupled to the vibrating surface.

19. The method ofclaim 18 wherein the disc has a periphery, and wherein the disc is heated proximate the periphery.

20. The method ofclaim 19 wherein the disc is heated by a focused laser.

21. The method ofclaim 20 wherein the laser intensity is modulated at approximately twice the resonant frequency of the micromechanical oscillator.

22. The method ofclaim 20 wherein the laser is also used to sense movement of the disc.

23. A method of sensing vibrations, the method comprising:

locating a micromechanical oscillator proximate a vibrating surface;

changing an effective stiffness of the micromechanical oscillator;

sensing vibration of the micromechanical oscillator; and

modulating the effective stiffness based on the sensed vibration.

24. A parametric oscillator comprising:

a micromechanical oscillator;

means for modifying a resonant frequency of the micromechanical oscillator;

means for measuring movement of the oscillator; and

means for driving the means for modifying based on measured movement of the oscillator or a reference signal.

25. The parametric oscillator ofclaim 24 wherein the micromechanical oscillator comprises a disc supported by a pillar.

26. The parametric oscillator ofclaim 25 wherein the disc is formed of single crystal silicon and the pillar is formed of silicon oxide.

27. The parametric oscillator ofclaim 24 wherein the means for modifying the resonant frequency comprises a laser focused on a selected portion of the micromechanical oscillator.

28. A receiver comprising:

an antenna;

a micromechanical oscillator coupled to the antenna;

a laser focused on a predetermined portion of the oscillator to modify its resonant frequency;

a detector that detects oscillation of the oscillator; and

a frequency multiplier that modifies the intensity of the laser at approximately twice the frequency of the detected oscillation of the oscillator.

29. A method of sensing vibrations, the method comprising:

locating a micromechanical oscillator proximate a vibrating surface;

changing an effective stiffness of the micromechanical oscillator by heating it with a laser; and

sensing vibration of the micromechanical oscillator

30. The method ofclaim 29 wherein the laser power is below a self generation threshold and the power is varied at approximately twice the resonant frequency of the micromechanical oscillator.

31. The method ofclaim 29 wherein the laser power is above a self generation threshold to promote self oscillation of the micromechnical oscillator.

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